Volume Radius Problem: Solving with Cylindrical Method

[frozen7]

The volume surrounded by y = x^2 , y=0, x=-2, x=-1 , revolved about y axis,by using cylindrical method.

The region is actually within x=-1 to -2 and it can actually same with x=1 to 2.

radius = 2-x
height = x^2

Is my assumption correct?

 

[Fermat]

Your radius should simply be x. With limits of: x = 1 to 2

You assumption about being able to use the region in the 1st quadrant is correct, yes.

 

[frozen7]

How come the radius should be x?

 

[Fermat]

The radius should be x because the radius of the cylinder is the distance from the origin.
The volume of revolution is about the y-axis, which passes through the origin. And you are finding the volumes of all the thin cylinders starting with cylinders with a radius of x = 1 to x= 2.

See here for a further treatment of the cylindrical method.

 

[frozen7]

Something wrong with the link you have given.

 

[Fermat]

Sorry 'bout that. Forgot to add in the url.
The link is fixed now.